YIELD CURVE GENERATION

Size: px
Start display at page:

Download "YIELD CURVE GENERATION"

Transcription

1 1 YIELD CURVE GENERATION Dr Philip Symes

2 Agenda 2 I. INTRODUCTION II. YIELD CURVES III. TYPES OF YIELD CURVES IV. USES OF YIELD CURVES V. YIELD TO MATURITY VI. BOND PRICING & VALUATION

3 Introduction 3 A yield curve is a graphical depiction of the relationship between the yield on a class of Securities for different maturities. Rate (%) Overnight Rate Time 10 Year Bond

4 Introduction 4 Types of yield curves (hypothetical): Normal Inverted YTM YTM Maturity Maturity YTM Humped YTM Flat Maturity Maturity

5 Yield Curves 5 Theories Explaining Shapes of Yield Curves: Liquidity Preference Investors prefer liquidity upward sloping yield curve Pure Expections Theory Term structure reflects market s current expectation of future rates Market Segmentation Theory Shape is determined by supply of and demand for securities within each maturity sector Shape of the yield curve is best explained by a combination of the three aforementioned theories.

6 Yield Curves 6 External Factors Affecting Yield Curves: Central Bank Policy Inflation Concerns Liquidity Desires Supply/Demand Conditions.

7 Types of Yield Curves 7 Coupon Bearing Yield Curves: The coupon bearing yield curve is derived from observable market bond yields at various terms to maturity. The yield to maturity of coupon bearing Government bonds of various maturities are normally used to construct the coupon bearing yield curve.

8 Types of Yield Curves 8 Zero Coupon Rate: The zero coupon rate gives the annualised interest rate receivable on a deposit starting immediately where the interest is payable at the maturity date. It can be used to calculate the amount that should be placed on deposit now to produce a fixed amount in time, i.e. to calculate the net present value of a single cash-flow. It will be higher than the annualised coupon rate on tenors over one year to compensate investors for not receiving any cashflows before maturity.

9 Types of Yield Curves 9 Forward Rate Curve: The forward interest rate is the interest implied (using arbitrage theory) by the zero coupon rates for periods of time in the future. An example of a forward rate is the interest rate for a deposit starting in 3 months time for a period of 3 months. Zero Coupon Rate Yield for deposit to t Yield for deposit to t-p t-p t { p Term to Maturity

10 Types of Yield Curves 10 Forward Rate Example: What is the forward rate for a 3 month deposit starting in 9 months and maturing in 12 months given the following yield curve? Period Zero Coupon Rate Months %

11 Types of Yield Curves 11 Forward Rate Example (cont.): Return on a 12 month deposit = 100 x ( %) Return on a 9 month deposit followed by a 3 month deposit = 100 x ((1 + (8.30% x 274))x (1 + (r% x 91))) Where r = forward rate for a 3 month deposit starting in 9 months. r ={( (1+(0.085*365/365)) )-1}*(365/91) (1+(0.083*274/365)) = 8.568% This shows how the marginal forward rate has to rise above the one year rate so that the rate over the first 9 months is raised sufficiently to average 8.5% over a 12 month period.

12 Uses of Yield Curves 12 The Importance of Yield Curves: Swap valuation requires derivation of the zero coupon yield curve and forward rates. Zero coupon rates are used to calculate discount factors while forward rates are used to forecast the floating payments of the swap. All three yield curves have an upward sloping shape derived from observable market information. Rate Forward rate Zero-coupon yield Coupon-bearing bond yield Maturity

13 Uses of Yield Curves 13 Separate yield curves exist for: Interbank lending/borrowing rates Yields on government bills/notes/bonds Eurocommercial paper/notes/bonds Swaps (Government Bond yield plus a swap spread or swap rates) These reflect the different credit standing and tenor of various borrowers. Future prices LIBOR rates (annual + actual/360) Bond yields (semi-annual + 30/360) Swap rates Yield curve generator Zero-coupon yield curve (annual + actual /actual basis)

14 Uses of Yield Curves 14 Period yrs Sources Interest rate swaps usually use the swaps yield curve. The inputs to swaps yield curves come from different sources. 0-1 Interbank deposit rates (LIBOR, BA s, etc.) Interest rate future prices (Dollars, Sterling, French Franc and ECUs) 1-3 Interest rate futures FRA quotes Indicative swap rates Government bond yields plus a (quoted) swap spread 3-10 Indicative swap rates Government bond yields plus a swap spread Direct telephone quotes of swap rates Government bond yields plus a swap spread

15 Uses of Yield Curves 15 To derive the zero coupon yield curve the various inputs (BA s, bond, yields, futures, swap spreads) are utilised. To calculate the various yield curves (forward rate, zero coupon) we must know: the basis of the various inputs (zero coupon, coupon bearing) compounding frequency (annual, continuous) day count convention (A/360, A/365) Once we know whether a various input is a zero coupon, bond yield or forward rate one can construct the zero coupon yield curve by using a variety of formulas.

16 Uses of Yield Curves 16 A futures contract that matures in 3 months A 3 month futures contract is a contract on a 3 month deposit starting in 3 months time Forward rate A 2 year Government of Canada Bond yield Coupon bearing A 5 year swap spread quoted by a broker Coupon bearing A 6-12 FRA Forward rate A 12 month BA deposit rate Zero coupon A 1 year swap rate quote Coupon bearing

17 Uses of Yield Curves 17 In deriving yield curves it is also very important to be able to convert between different coupon bearing rates. Rates can be quoted as: continuously compounded Annualised Semi-annual Quarterly simple interest Rates can also be quoted on different day count conventions: Actual/360 actual/365 actual/actual 30/360

18 Uses of Yield Curves 18 Example: Take a 2-year Government of Canada semi-annual bond yield of 8%: Annualised: (1 + r / 2 ) 2 1 = 8.16% Simple Interest: Continously Compounded: [(1 + r / 2 ) 4 1] = 8.493% 2 2 ln (1 + r / 2 ) = 7.844% remember the inverse of Ln(x) is e x If the annual yield is 8.16% on an actual/365 basis, what is it on an actual/360 basis? 8.16% x 360/365 = 8.048%

19 Uses of Yield Curves 19 Examples: 5-year Government of Canada semi annual yield is 10%. What is the quarterly compounded rate? Annual Yield = (1 + 10% / 2 ) 2 1 = 10.25% quarterly compounded 4[(1.1025) ] = 9.878% or 4[( / 2 ) 0.5 1] = 9.878% A continous compounded interest rate is 20%, what is the equivalent weekly interest rate? 52 (e 0.2/52 1) = % Annual yield on a bond is 50%, what is the continously compounded yield? ln ( ) = %

20 Yield to Maturity 20 Yield to Maturity: In constructing a yield curve one of the inputs used is the yield to maturity of various Government bonds. The yield to maturity of a bond is equivalent to its internal rate of return. It represents the notional rate of interest at which all cash flows receivable during the life of the bond should be discounted to give the market value of the bond. It assumes a flat yield curve.

21 Yield to Maturity 21 Credit Spreads Counterparties with different credit standing and different tenors of debt will show different yields to maturity as a result. YTM B BB BBB A AA AAA Govt. of Canada Maturity (in years)

22 Yield to Maturity 22 A bond with a price of par ($100) and an annual coupon of 8% has a yield to maturity of 8%. If the bond price was $110 then the yield to maturity would be less than 8%. In simple terms the investment of $110 is yielding $8 in value per year. Therefore its yield as a percentage of the investment is less than 8%. Bond Price Bond yield/interest rates

23 Yield to Maturity 23 Calculation of Yield-to-Maturity: Bond Price = C + C C (1+Y) 1 (1+Y) 2 (1+Y) n where, C = Coupon (annual) Y = Yield to maturity To calculate the yield to maturity of a bond requires an iterative process i.e., trial and error.

24 Yield to Maturity 24 A three year bond, paying an annual coupon of 10% has a price of $110. What is the yield to maturity? Try 5%, = (1.05) 2 (1.05) 3 Try 6%, = (1.06) 2 (1.06) 3 Actually it is 6.242% = ( ) 2 ( ) 3

25 Bond Yields & Values 25 Bond Yields: Why do we need to know yields on bonds? We use them to calculate zero coupon interest rates and therefore the yield curve. A 3 year bond with a coupon of 10% and a price of $110 is the same as a 3 year bond with a coupon of 6.242% and a price $100. The yield to maturity gives us the equivalent annually compounded coupon of an investment of $100. We can use this to construct our yield curve.

26 Bond Yields & Values 26 Bond Valuation: The mathematics of bond valuation are also very important in deriving a yield curve. A bond is just a series of cash flows (coupon and principal). The value of the bond is the discounted value of each cash flow. As we have seen by discounting each cash flow at the yield to maturity gives us the bond value. We can also value a bond by discounting each cash flow using the zero coupon interest rate equivalent to each cash flow s maturity.

27 Bond Yields & Values 27 Example: Bond Maturity = 3 years Coupon = 10% annually Zero Coupon Rates End of Year 1 7% 2 9% 3 11% Bond Value = = (1.07) (1.09) 2 (1.11) 3

28 Bond Yields & Values 28 Derivation of a Yield Curve: Using bond yields and BA deposit rates we are going to derive a zero-coupon yield curve. The zero coupon yield curve can then be used to calculate forward rates and discount factors which will then be used to value a swap. As we have already seen the inputs are used by valuation models such as Oberon to calculate a zero coupon yield curve. Future prices LIBOR rates (annual + actual/360) Bond yields (semi-annual + A/365) Yield curve generator Zero-coupon yield curve (annual + actual /365 basis) Swap rates

29 Bond Yields & Values 29 Example: The inputs are: BA Deposit Rates (A/360) 1 month 5.346% 3 months 5.395% 6 months 5.494% 9 months 5.573% 12 months 5.622% Bond Yields plus swap spreads (semi-annual, A/365) Bond Yield Swap Spread Add-in 2 year 5.86% 0.04% 5.9 % 3 year 6.13% 0.04% 6.17% 4 year 6.34% 0.06% 6.40% 5 year 6.54% 0.10% 6.64%

30 Bond Yields & Values Conversion of Semi-Annual Yields to Annual and A/360 to A/365 The bond yields and swap spreads are quoted on a semi-annual basis. The initial step (for simplicity) is to convert these to an annual yield as follows: 2 year rate ( ( = 5.987% 1 2 The BA deposit rates are quoted as A/360, therefore they need converting to A/365 1 month rate 5.346% x 365 / 360 = 5.42% Converted Rates: Bond Yields and Swap Spreads 2 year 5.987% 3 year 6.265% 4 year 6.502% 5 year 6.75% BA Deposit Rates 1 month 5.42% 3 months 5.47% 6 months 5.57% 9 months 5.65% 12 months 5.70% 30

31 Bond Yields & Values 31 Boot-Strap Technique The BA deposit rates are now in zero coupon format and on an A/365 basis. No further calculation is required. Beyond 12 months we have coupon bearing yields on an annual A/365 basis. The method we use to calculate zero coupon rates beyond one year is called the boot-strap technique. It is similar to the method we used to value a bond. As you remember the formula for valuing a bond was: Price = C + C C + P 1 + r 1 (1+r 2 ) 2 (1+r n ) n where, C = Coupon r = Zero coupon rate at each maturity P = Principal

32 Bond Yields & Values 32 We also know that the bond yield is the coupon which returns a price for the bond of $100 (par). We can now use this formula to calculate zero coupon rates beyond one year. 2 year point Coupon = 5.987% = 100 Price = $100 (1+r 1 ) (1+r 2 ) = 100 ( ) (1+r 2 ) 2 rearranging formula, = (1+r 2 ) 2 = (1+r 2 ) r 2 = ( ^ 0.5) 1 r 2 = 5.995%

33 Bond Yields & Values 33 The same technique applies to 3, 4 and 5 years. Our zero coupon yield curve (A/365 is as follows: 1 month 5.42% 3 months 5.47% 6 months 5.59% 9 months 5.65% 12 months 5.70% 2 year 6.00% 3 years 6.29% 4 years 6.55% 5 years 6.82%

34 Bond Yields & Values 34 More Advanced Techniques: The zero-coupon rates we have calculated are for specific dates. If we required a rate between two points the easiest method is to linearly interpolate. Yield curve generators such as Oberon have more advanced methods of interpolation between rates and calculating yield curves. Log-linear interpolation and Cubic Spline : These introduce a curve between two points rather than a straight line. Cubic Spline Linear d 1 d x d 2

35 Bond Yields & Values 35 Which Instruments to Use Depends on the Curve Being Constructed Most liquid instruments indicates real market probably most usable as hedges Relevant credit rating/index type LIBOR based instruments Government based instruments Quoted IR Products Cash (Libor or BA loans and deposits) Futures (e.g. LIFFE traded contracts) and FRA s Commercial Paper and CD s Government Stock (e.g. T-Bills and Gilts) Swaps (if liquid secondary markets)

36 Summary 36 Yield curves are widely used to price bonds and other interest rate products. Yield curves are graphical descriptions of the relationship between interest rate payments and maturity. There are different yield curves for coupon bonds, zero bonds and forward rate products. Yield-to-maturity is defined as the percentage return on a product if held to maturity This assumes no reinvestment risk of coupon payments. Yield curves are used for comparing the price payoff of different products I.e. for pricing products at different maturities. Different methods exist for interpolating yield curves to price products.

Chapter 4 Interest Rates. Options, Futures, and Other Derivatives 9th Edition, Copyright John C. Hull

Chapter 4 Interest Rates. Options, Futures, and Other Derivatives 9th Edition, Copyright John C. Hull Chapter 4 Interest Rates 1 Types of Rates! Treasury rate! LIBOR! Fed funds rate! Repo rate 2 Treasury Rate! Rate on instrument issued by a government in its own currency 3 LIBOR! LIBOR is the rate of interest

More information

Problem Set 2. Econ 236

Problem Set 2. Econ 236 Problem Set 2 Econ 236 Question 1............................................................................. 10 points On 22 April 2016, the settlement prices for the Jun 2016, Sep 2016 and Dec 2016

More information

Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates

Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment

More information

Chapter 9 Contents. 1. Identify the key features of bonds and describe differences between private and public debt markets.

Chapter 9 Contents. 1. Identify the key features of bonds and describe differences between private and public debt markets. Chapter 9 Debt Valuation and Interest Rates Chapter 9 Contents Learning Objectives 1. Overview of Corporate Debt 1. Identify the key features of bonds and describe differences between private and public

More information

Chapter 4 Interest Rates. Options, Futures, and Other Derivatives 8th Edition, Copyright John C. Hull

Chapter 4 Interest Rates. Options, Futures, and Other Derivatives 8th Edition, Copyright John C. Hull Chapter 4 Interest Rates 1 Types of Rates Treasury rates LIBOR rates Repo rates 2 Treasury Rates Rates on instruments issued by a government in its own currency 3 LIBOR and LIBID LIBOR is the rate of interest

More information

FIN 472 Fixed-Income Securities Debt Instruments

FIN 472 Fixed-Income Securities Debt Instruments FIN 472 Fixed-Income Securities Debt Instruments Professor Robert B.H. Hauswald Kogod School of Business, AU The Most Famous Bond? Bond finance raises the most money fixed income instruments types of bonds

More information

ACI THE FINANCIAL MARKETS ASSOCIATION

ACI THE FINANCIAL MARKETS ASSOCIATION ACI THE FINANCIAL MARKETS ASSOCIATION EXAMINATION FORMULAE 2009 VERSION page number INTEREST RATE..2 MONEY MARKET..... 3 FORWARD-FORWARDS & FORWARD RATE AGREEMENTS..4 FIXED INCOME.....5 FOREIGN EXCHANGE

More information

FIXED-INCOME SECURITIES. Chapter 10. Swaps

FIXED-INCOME SECURITIES. Chapter 10. Swaps FIXED-INCOME SECURITIES Chapter 10 Swaps Outline Terminology Convention Quotation Uses of Swaps Pricing of Swaps Non Plain Vanilla Swaps Terminology Definition Agreement between two parties They exchange

More information

Chapter Nine Selected Solutions

Chapter Nine Selected Solutions Chapter Nine Selected Solutions 1. What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the

More information

Bond valuation and bond yields

Bond valuation and bond yields RELEVANT TO ACCA QUALIFICATION PAPER P4 AND PERFORMANCE OBJECTIVES 15 AND 16 Bond valuation and bond yields Bonds and their variants such as loan notes, debentures and loan stock, are IOUs issued by governments

More information

Using the bond valuation formulas (7.1), (7.3), (7.6) we obtain the following yields and prices: Zero-Coupon Bond Price

Using the bond valuation formulas (7.1), (7.3), (7.6) we obtain the following yields and prices: Zero-Coupon Bond Price Chapter 7 Interest Rate Forwards and Futures Question 7.1 Using the bond valuation formulas (7.1), (7.3), (7.6) we obtain the following yields and prices: Maturity Bond Yield Bond Price One-Year Implied

More information

Chapter 11. Bond Pricing - 1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions.

Chapter 11. Bond Pricing - 1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions. Bond Pricing - 1 Chapter 11 Several Assumptions: To simplify the analysis, we make the following assumptions. 1. The coupon payments are made every six months. 2. The next coupon payment for the bond is

More information

Outline. Main Features of Bonds. Fixed-Income Securities. Professor Lasse H. Pedersen

Outline. Main Features of Bonds. Fixed-Income Securities. Professor Lasse H. Pedersen Fixed-Income Securities Professor Lasse H. Pedersen Prof. Lasse H. Pedersen 1 Outline Main features of bonds Yield to maturity Realized return Forward rates Yield curve or term structure of interest Prof.

More information

INTEREST RATE SWAPS September 1999

INTEREST RATE SWAPS September 1999 INTEREST RATE SWAPS September 1999 INTEREST RATE SWAPS Definition: Transfer of interest rate streams without transferring underlying debt. 2 FIXED FOR FLOATING SWAP Some Definitions Notational Principal:

More information

Margin Calculation Methodology and Derivatives and Repo Valuation Methodology

Margin Calculation Methodology and Derivatives and Repo Valuation Methodology Margin Calculation Methodology and Derivatives and Repo Valuation Methodology 1 Overview This document presents the valuation formulas for interest rate derivatives and repo transactions implemented in

More information

Notes for Lecture 3 (February 14)

Notes for Lecture 3 (February 14) INTEREST RATES: The analysis of interest rates over time is complicated because rates are different for different maturities. Interest rate for borrowing money for the next 5 years is ambiguous, because

More information

Valuation of a Forward Rate Agreement (pp )

Valuation of a Forward Rate Agreement (pp ) Valuation of a Forward Rate Agreement (pp. 95-96) A forward-rate agreement (FRA) is a forward contract where it is agreed that a certain interest rate R K will apply to a certain principal to a specified

More information

Chapter 3 Fixed Income Securities

Chapter 3 Fixed Income Securities Chapter 3 Fixed Income Securities Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixed-income securities. Stocks. Real assets (capital budgeting). Part C Determination

More information

Bonds. Finance 100. Prof. Michael R. Roberts. Topic Overview

Bonds. Finance 100. Prof. Michael R. Roberts. Topic Overview Bonds Finance 100 Prof. Michael R. Roberts 1 Topic Overview Introduction to bonds and bond markets Zero coupon bonds» Valuation» Yield-to-Maturity & Yield Curve» Spot Rates» Interest rate sensitivity DVO1

More information

FIN 350 Business Finance Homework 3 Fall 2014 Solutions

FIN 350 Business Finance Homework 3 Fall 2014 Solutions FIN 350 Business Finance Homework 3 Fall 014 Solutions 1. The yield to maturity of a $1,000 bond with a 7% coupon rate, semi-annual coupons and two years to maturity is 7.6% APR, compounded semi-annually.

More information

FNCE 301, Financial Management H Guy Williams, 2006

FNCE 301, Financial Management H Guy Williams, 2006 REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including

More information

Introduction to Bond Valuation. Types of Bonds

Introduction to Bond Valuation. Types of Bonds Introduction to Bond Valuation (Text reference: Chapter 5 (Sections 5.1-5.3, Appendix)) Topics types of bonds valuation of bonds yield to maturity term structure of interest rates more about forward rates

More information

a) The government offers I-Bonds. These bonds are identical to the usual government bonds, except that they are inflation adjusted.

a) The government offers I-Bonds. These bonds are identical to the usual government bonds, except that they are inflation adjusted. Chapter 6 Interest Rates and Bond Valuation 1) What is the real rate of interest? Can this rate be controlled? Base rate created by supply and demand Extremely low now (.3 to.5%) 2) What is the risk free

More information

Chapter 8 Interest Rates and Bond Valuation

Chapter 8 Interest Rates and Bond Valuation University of Science and Technology Beijing Dongling School of Economics and management Chapter 8 Interest Rates and Bond Valuation Oct. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Know the important

More information

Bond Prices and Yields

Bond Prices and Yields 14-2 Bond Characteristics Bond Prices and Yields Bonds are debt. Issuers are borrowers and holders are creditors. The indenture is the contract between the issuer and the bondholder. The indenture gives

More information

Yield Measures, Spot Rates & Forward Rates

Yield Measures, Spot Rates & Forward Rates Fixed Income Yield Measures, Spot Rates & Forward Rates Reading - 57 www.proschoolonline.com/ 1 Sources of Return Coupon interest payment: Periodic coupon interest is paid on the par value of the bond

More information

Chapter 6. Interest Rates And Bond Valuation. Learning Goals. Learning Goals (cont.)

Chapter 6. Interest Rates And Bond Valuation. Learning Goals. Learning Goals (cont.) Chapter 6 Interest Rates And Bond Valuation Learning Goals 1. Describe interest rate fundamentals, the term structure of interest rates, and risk premiums. 2. Review the legal aspects of bond financing

More information

Total return swap. Exchange the total economic performance of a specific asset for another cash flow. total return of asset.

Total return swap. Exchange the total economic performance of a specific asset for another cash flow. total return of asset. Total return swap Exchange the total economic performance of a specific asset for another cash flow. Total return payer total return of asset LIBOR + Y bp Total return receiver Total return comprises the

More information

Financial Mathematics for Actuaries. Chapter 7 Bond Yields and the Term Structure

Financial Mathematics for Actuaries. Chapter 7 Bond Yields and the Term Structure Financial Mathematics for Actuaries Chapter 7 Bond Yields and the Term Structure 1 Learning Objectives 1. Yield to maturity, yield to call and par yield 2. Realized compound yield and horizon analysis

More information

Fixed Income: Practice Problems with Solutions

Fixed Income: Practice Problems with Solutions Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semi-annual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.

More information

Understanding Fixed Income

Understanding Fixed Income Understanding Fixed Income 2014 AMP Capital Investors Limited ABN 59 001 777 591 AFSL 232497 Understanding Fixed Income About fixed income at AMP Capital Our global presence helps us deliver outstanding

More information

INVESTMENTS Classe 15: Forwards, Futures & Swaps. Spring 2003

INVESTMENTS Classe 15: Forwards, Futures & Swaps. Spring 2003 15.433 INVESTMENTS Classe 15: Forwards, Futures & Swaps Spring 2003 Interest Rate Derivatives Interest rate swaps, caps, floors, and swaptions are over the counter (OTC) interest rate derivatives. Broadly

More information

Key Terms bond certificate p. 170

Key Terms bond certificate p. 170 194 Chapter 6 Valuing Bonds When the yield curve is not flat, bonds with the same maturity but different coupon rates will have different yields to maturity. 6.4 Corporate Bonds When a bond issuer does

More information

Chapter 6. Interest Rates and Bond Valuation

Chapter 6. Interest Rates and Bond Valuation Chapter 6 Interest Rates and Bond Valuation Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean

More information

CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING

CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING Topic One: Bond Pricing Principles 1. Present Value. A. The present-value calculation is used to estimate how much an investor should pay for a bond;

More information

NOTES ON THE BANK OF ENGLAND UK YIELD CURVES

NOTES ON THE BANK OF ENGLAND UK YIELD CURVES NOTES ON THE BANK OF ENGLAND UK YIELD CURVES The Macro-Financial Analysis Division of the Bank of England estimates yield curves for the United Kingdom on a daily basis. They are of three kinds. One set

More information

Relative value analysis: calculating bond spreads Moorad Choudhry January 2006

Relative value analysis: calculating bond spreads Moorad Choudhry January 2006 Relative value analysis: calculating bond spreads Moorad Choudhry January 2006 Relative value analysis: bond spreads Moorad Choudhry Investors measure the perceived market value, or relative value, of

More information

FINANCIAL MATHEMATICS MONEY MARKET

FINANCIAL MATHEMATICS MONEY MARKET FINANCIAL MATHEMATICS MONEY MARKET 1. Methods of Interest Calculation, Yield Curve and Quotation... 2 1.1 Methods to Calculate Interest... 2 1.2 The Yield Curve... 6 1.3 Interpolation... 8 1.4 Quotation...

More information

Chapter 9 Contents. 1. Identify the key features of bonds and describe differences between private and public debt markets.

Chapter 9 Contents. 1. Identify the key features of bonds and describe differences between private and public debt markets. Chapter 9 Debt Valuation and Interest Rates Chapter 9 Contents Learning Objectives 1. Overview of Corporate Debt 1. Identify the key features of bonds and describe differences between private and public

More information

FIN Chapter 9. Debt Valuation and Interest Rates. Liuren Wu

FIN Chapter 9. Debt Valuation and Interest Rates. Liuren Wu FIN 3000 Chapter 9 Debt Valuation and Interest Rates Liuren Wu Overview 1. Overview of Corporate Debt Identify the key features of bonds and describe the difference between private and public debt markets.

More information

ANALYSIS OF FIXED INCOME SECURITIES

ANALYSIS OF FIXED INCOME SECURITIES ANALYSIS OF FIXED INCOME SECURITIES Valuation of Fixed Income Securities Page 1 VALUATION Valuation is the process of determining the fair value of a financial asset. The fair value of an asset is its

More information

CURRENT STANDARDS ON FIXED INCOME

CURRENT STANDARDS ON FIXED INCOME CURRENT STANDARDS ON FIXED INCOME PRICING FIXED INCOME SECURITIES AGAINST AN INTEREST SWAP CURVE December 2012 CNO Association régie par la loi du 1 er juillet 1901 8 rue du Mail 75002 Paris http://www.cnofrance.org

More information

Money Market and Debt Instruments

Money Market and Debt Instruments Prof. Alex Shapiro Lecture Notes 3 Money Market and Debt Instruments I. Readings and Suggested Practice Problems II. Bid and Ask III. Money Market IV. Long Term Credit Markets V. Additional Readings Buzz

More information

ILLUSTRATING SPOT AND FORWARD INTEREST RATES Learning Curve August 2003

ILLUSTRATING SPOT AND FORWARD INTEREST RATES Learning Curve August 2003 ILLUSTRATING SPOT AND FORWARD INTEREST RATES Learning Curve August 003 Practitioners in the bond markets need to determine the true interest rate for any period or term to maturity, for a number of applications.

More information

Swaps Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012

Swaps Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012 Swaps Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012 Introduction A swap is an OTC agreement between two companies to exchange cash flows in the future. The agreement

More information

Figure 10.1 Listing of Treasury Issues

Figure 10.1 Listing of Treasury Issues CHAPER 10 Bond Prices and Yields 10.1 BOND CHARACERISICS Bond Characteristics reasury Notes and Bonds Face or par value Coupon rate Zero coupon bond Compounding and payments Accrued Interest Indenture

More information

Asset-backed security (ABS): A pass-through security that represents an interest in non-mortgage financial assets.

Asset-backed security (ABS): A pass-through security that represents an interest in non-mortgage financial assets. Debt Glossary American-style call feature: The call option may be exercised on any business day after an initial lockout period. This type of call feature is also referred to as a continuous call. Asset-backed

More information

Solutions to Problems

Solutions to Problems Solutions to Problems P6-1. LG 1: Yield curve b. The yield curve is slightly downward sloping, reflecting lower expected future rates of interest. The curve may reflect a general expectation for an economic

More information

FIN 472 Fixed-Income Securities Forward Rates

FIN 472 Fixed-Income Securities Forward Rates FIN 472 Fixed-Income Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU Interest-Rate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward

More information

Finance for Cultural Organisations Lecture 5. Interest Rates and Bond Valuation

Finance for Cultural Organisations Lecture 5. Interest Rates and Bond Valuation Finance for Cultural Organisations Lecture 5. Interest Rates and Bond Valuation Lecture 5: Interest Rates and Bond Valuation Know the important bond features and bond types Understand bond values and why

More information

CHAPTER 9 DEBT SECURITIES. by Lee M. Dunham, PhD, CFA, and Vijay Singal, PhD, CFA

CHAPTER 9 DEBT SECURITIES. by Lee M. Dunham, PhD, CFA, and Vijay Singal, PhD, CFA CHAPTER 9 DEBT SECURITIES by Lee M. Dunham, PhD, CFA, and Vijay Singal, PhD, CFA LEARNING OUTCOMES After completing this chapter, you should be able to do the following: a Identify issuers of debt securities;

More information

Chapter 7 Swaps. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull

Chapter 7 Swaps. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull Chapter 7 Swaps 1 Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules 2 An Example of a Plain Vanilla Interest Rate Swap! An agreement

More information

Interest Rates and Bond Valuation

Interest Rates and Bond Valuation Interest Rates and Bond Valuation Chapter 6 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean

More information

CFAspace. CFA Level II. Provided by APF. Academy of Professional Finance 专业金融学院

CFAspace. CFA Level II. Provided by APF. Academy of Professional Finance 专业金融学院 CFAspace Provided by APF CFA Level II Fixed Income: The Term Structure and Interest Rate Dynamics Lecturer: Nan Chen Framework Reading Reading: The Term Structure and Interest Rate Dynamics Reading: Spot

More information

YTM 9.993% 9.660% 8.995% 8.000% Time to Maturity

YTM 9.993% 9.660% 8.995% 8.000% Time to Maturity Fi8000 Valuation of Financial Assets Fall Semester 2009 Dr. Isabel Tkatch Assistant Professor of Finance Types of bonds Debt instruments Ratings of bonds (default risk) Spot and forward interest rate The

More information

1. An insurance company earned a simple rate of interest of 8% over the last calendar year. Assets, beginning of year 25,000,000 Sales revenue

1. An insurance company earned a simple rate of interest of 8% over the last calendar year. Assets, beginning of year 25,000,000 Sales revenue Exam FM November 2005 1. An insurance company earned a simple rate of interest of 8% over the last calendar year based on the following information: Assets, beginning of year 25,000,000 Sales revenue X

More information

Tenor Adjustments for a Basis Swap

Tenor Adjustments for a Basis Swap Tenor Adjustments for a Basis Swap by Chandrakant Maheshwari Praveen Maheshwari Table of Contents 1. Introduction 3 2. Tenor Adjustment Methodology for a Basis Swap 3 3. Why this Tenor Spread so important

More information

Interest Rate Swaps Currency Swaps Forward Rate Agreements

Interest Rate Swaps Currency Swaps Forward Rate Agreements Derivatives Interest Rate Swaps Currency Swaps Forward Rate Agreements cesariomateus@gmail.com www.cesariomateus.com 1 Swaps Plain vanilla Interest rate swap (most common type of swap). Company agrees

More information

Spring 2004 Casualty Actuarial Society Course 8 Examination, Problem No. 22 Spring 2004 Casualty Actuarial Society Course 8 Examination, Problem No.

Spring 2004 Casualty Actuarial Society Course 8 Examination, Problem No. 22 Spring 2004 Casualty Actuarial Society Course 8 Examination, Problem No. Below you will find exercises on topics of MAT 483, written as multiple choice problems, with solutions. Please use these exercises in preparation for the final examinations. Additionally, please study

More information

Investment Management Bond Portfolio Management

Investment Management Bond Portfolio Management Investment Management Bond Portfolio Management Road Map Bond markets Bond Yields Bond Pricing: Zero-coupon bonds, Coupon bonds Price sensitivity Duration and Convexity The term structure of interest rates

More information

Case 11-2(a) Fair Value Hierarchy

Case 11-2(a) Fair Value Hierarchy Case 11-2(a) Fair Value Hierarchy Family Finance Co. (FFC), a publicly traded commercial bank located in South Carolina, has a December 31 year-end. FFC invests in a variety of securities to enhance returns,

More information

What is a Swap? A swap is an agreement to exchange cash flows in the future according to specified rules.

What is a Swap? A swap is an agreement to exchange cash flows in the future according to specified rules. 3. Swaps What is a Swap? A swap is an agreement to exchange cash flows in the future according to specified rules. Plain Vanilla and Currencies Cash flows can be positive (investment) or negative (liability).

More information

1. An insurance company earned a simple rate of interest of 8% over the last calendar year. Assets, beginning of year 25,000,000 Sales revenue

1. An insurance company earned a simple rate of interest of 8% over the last calendar year. Assets, beginning of year 25,000,000 Sales revenue Exam FM November 2005 1. An insurance company earned a simple rate of interest of 8% over the last calendar year based on the following information: Assets, beginning of year 25,000,000 Sales revenue X

More information

INSTITUTE OF ECONOMIC STUDIES

INSTITUTE OF ECONOMIC STUDIES INSTITUTE OF ECONOMIC STUDIES Faculty of social sciences of Charles University Swaps Lecturer s Notes No. 4 Course: Financial Market Instruments II Teacher: Oldřich Dědek VII. INTEREST RATE SWAPS 7.1 The

More information

Chapter 6 Interest Rates and Bond Valuation

Chapter 6 Interest Rates and Bond Valuation Chapter 6 Interest Rates and Bond Valuation Solutions to Problems P6-1. P6-2. LG 1: Interest Rate Fundamentals: The Real Rate of Return Basic Real rate of return = 5.5% 2.0% = 3.5% LG 1: Real Rate of Interest

More information

Learning Curve September 2005. Understanding the Z-Spread Moorad Choudhry*

Learning Curve September 2005. Understanding the Z-Spread Moorad Choudhry* Learning Curve September 2005 Understanding the Z-Spread Moorad Choudhry* A key measure of relative value of a corporate bond is its swap spread. This is the basis point spread over the interest-rate swap

More information

Swaps. Chapter 7 7.1

Swaps. Chapter 7 7.1 Swaps Chapter 7 7.1 Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules 7.2 An Example of a Plain Vanilla Interest Rate Swap An

More information

Chapter 5: Valuing Bonds

Chapter 5: Valuing Bonds FIN 302 Class Notes Chapter 5: Valuing Bonds What is a bond? A long-term debt instrument A contract where a borrower agrees to make interest and principal payments on specific dates Corporate Bond Quotations

More information

Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage

Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage Prof. Alex Shapiro Lecture Notes 12 Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage I. Readings and Suggested Practice Problems II. Bonds Prices and Yields (Revisited)

More information

Assumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk

Assumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk Derivatives Why? Allow easier methods to short sell a stock without a broker lending it. Facilitates hedging easily Allows the ability to take long/short position on less available commodities (Rice, Cotton,

More information

Bond Valuation. Chapter 7. Example (coupon rate = r d ) Bonds, Bond Valuation, and Interest Rates. Valuing the cash flows

Bond Valuation. Chapter 7. Example (coupon rate = r d ) Bonds, Bond Valuation, and Interest Rates. Valuing the cash flows Bond Valuation Chapter 7 Bonds, Bond Valuation, and Interest Rates Valuing the cash flows (1) coupon payment (interest payment) = (coupon rate * principal) usually paid every 6 months (2) maturity value

More information

2. Determine the appropriate discount rate based on the risk of the security

2. Determine the appropriate discount rate based on the risk of the security Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the

More information

Chapter 6 Interest Rate Futures. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull

Chapter 6 Interest Rate Futures. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull Chapter 6 Interest Rate Futures 1 Day Count Convention! Defines:! the period of time to which the interest rate applies! The period of time used to calculate accrued interest (relevant when the instrument

More information

Overview of Lecture 5 (part of Lecture 4 in Reader book)

Overview of Lecture 5 (part of Lecture 4 in Reader book) Overview of Lecture 5 (part of Lecture 4 in Reader book) Bond price listings and Yield to Maturity Treasury Bills Treasury Notes and Bonds Inflation, Real and Nominal Interest Rates M. Spiegel and R. Stanton,

More information

Chapter 14. Bond Prices and Yields

Chapter 14. Bond Prices and Yields Chapter 14 Bond Prices and Yields Bond Characteristics A bond is a security that is issued in connection with a borrowing arrangement. The borrower issues (i.e. sells) a bond to the lender for some amount

More information

Bond Valuation. Capital Budgeting and Corporate Objectives

Bond Valuation. Capital Budgeting and Corporate Objectives Bond Valuation Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Bond Valuation An Overview Introduction to bonds and bond markets» What

More information

3. instruments are also called fixed-income instruments. a. Debt b. Equity c. Derivative d. All of the above e. None of the above

3. instruments are also called fixed-income instruments. a. Debt b. Equity c. Derivative d. All of the above e. None of the above Exam #1 Economics 5000 Financial Economics Dr. Philip Rothman July 5, 2000 There are 25 questions on this exam. Record all of your answers on your blue bubble sheet. *********************************************************************************************************************

More information

Risk and Investment Conference 2013. Brighton, 17 19 June

Risk and Investment Conference 2013. Brighton, 17 19 June Risk and Investment Conference 03 Brighton, 7 9 June 0 June 03 Acquiring fixed income assets on a forward basis Dick Rae, HSBC and Neil Snyman, Aviva Investors 8 June 0 Structure of Presentation Introduction

More information

Answers to Review Questions

Answers to Review Questions Answers to Review Questions 1. The real rate of interest is the rate that creates an equilibrium between the supply of savings and demand for investment funds. The nominal rate of interest is the actual

More information

Global Financial Management

Global Financial Management Global Financial Management Bond Valuation Copyright 999 by Alon Brav, Campbell R. Harvey, Stephen Gray and Ernst Maug. All rights reserved. No part of this lecture may be reproduced without the permission

More information

Topics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk

Topics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk Bond Valuation 1 Topics in Chapter Key features of bonds Bond valuation Measuring yield Assessing risk 2 Determinants of Intrinsic Value: The Cost of Debt Net operating profit after taxes Free cash flow

More information

FIN221: Lecture 7 Notes. Bond Yields and Prices. Interest Rates. Interest Rates. Determinants of Interest Rates. Determinants of Interest Rates

FIN221: Lecture 7 Notes. Bond Yields and Prices. Interest Rates. Interest Rates. Determinants of Interest Rates. Determinants of Interest Rates FIN221: Lecture 7 Notes Bond Yields and Prices Chapters 8 and 9 Chapter 8 Charles P. Jones, Investments: Analysis and Management, Eighth Edition, John Wiley & Sons Prepared by G.D. Koppenhaver, Iowa State

More information

Bank of America AAA 10.00% T-Bill +.30% Hypothetical Resources BBB 11.90% T-Bill +.80% Basis point difference 190 50

Bank of America AAA 10.00% T-Bill +.30% Hypothetical Resources BBB 11.90% T-Bill +.80% Basis point difference 190 50 Swap Agreements INTEREST RATE SWAP AGREEMENTS An interest rate swap is an agreement to exchange interest rate payments on a notional principal amount over a specific period of time. Generally a swap exchanges

More information

Chapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23.

Chapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23. Chapter 8 Bond Valuation with a Flat Term Structure 1. Suppose you want to know the price of a 10-year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity

More information

1. A man borrows 1000 for 2 years at an annual effective rate of i. He has two payment options:

1. A man borrows 1000 for 2 years at an annual effective rate of i. He has two payment options: 1 Exam FM Questions Practice Exam 2 1. A man borrows 00 for 2 years at an annual effective rate of i. He has two payment options: 1. Pay 560 at the end of each year, or 2. Pay K at the end of year 1 and

More information

FIN 472 Fixed-Income Securities Forward Rates

FIN 472 Fixed-Income Securities Forward Rates FIN 472 Fixed-Income Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU Interest-Rate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward

More information

Problems and Solutions

Problems and Solutions Problems and Solutions CHAPTER Problems. Problems on onds Exercise. On /04/0, consider a fixed-coupon bond whose features are the following: face value: $,000 coupon rate: 8% coupon frequency: semiannual

More information

Chapter 6 Interest rates and Bond Valuation. 2012 Pearson Prentice Hall. All rights reserved. 4-1

Chapter 6 Interest rates and Bond Valuation. 2012 Pearson Prentice Hall. All rights reserved. 4-1 Chapter 6 Interest rates and Bond Valuation 2012 Pearson Prentice Hall. All rights reserved. 4-1 Interest Rates and Required Returns: Interest Rate Fundamentals The interest rate is usually applied to

More information

Learning Curve Forward Rate Agreements Anuk Teasdale

Learning Curve Forward Rate Agreements Anuk Teasdale Learning Curve Forward Rate Agreements Anuk Teasdale YieldCurve.com 2004 Page 1 In this article we review the forward rate agreement. Money market derivatives are priced on the basis of the forward rate,

More information

Chapter 4 Valuing Bonds

Chapter 4 Valuing Bonds Chapter 4 Valuing Bonds MULTIPLE CHOICE 1. A 15 year, 8%, $1000 face value bond is currently trading at $958. The yield to maturity of this bond must be a. less than 8%. b. equal to 8%. c. greater than

More information

THE COST OF MONEY (INTEREST RATES) [Chapter 5]

THE COST OF MONEY (INTEREST RATES) [Chapter 5] THE COST OF MONEY (INTEREST RATES) [Chapter 5] Cost of Money interest rate associated with borrowing funds. Realized Rates of Return returns include two components: (1) income paid by the issuer, and (2)

More information

Suggested Answers to Discussion Questions

Suggested Answers to Discussion Questions Suggested Answers to Discussion Questions 1. Expectations hypothesis: The yield curve reflects investor expectations above all else. Future behavior of interest rates with respect to the present is affected

More information

Introduction to Yield Curves

Introduction to Yield Curves Introduction to Yield Curves 1. Introduction A yield curve is a graphical representation of where interest rates are today. There is not one single interest rate; there is an interest rate for those who

More information

Chapter Nine Interest Rate Risk II

Chapter Nine Interest Rate Risk II Chapter Nine Interest Rate Risk II Chapter Outline Introduction Duration: A Simple Introduction A General Formula for Duration The Duration of Interest-Bearing Bonds The Duration of a Zero-Coupon Bond

More information

Fixed Income Glossary

Fixed Income Glossary Fixed Income Glossary AMP Capital Investors Limited ABN 59 001 777 591 AFSL 232497 Accrued interest Ask price Asset backed Bank capital Basis point Bearer bond Bid Bond Bond swap Call Callable bonds Cap

More information

Fixed Income Portfolio Management. Interest rate sensitivity, duration, and convexity

Fixed Income Portfolio Management. Interest rate sensitivity, duration, and convexity Fixed Income ortfolio Management Interest rate sensitivity, duration, and convexity assive bond portfolio management Active bond portfolio management Interest rate swaps 1 Interest rate sensitivity, duration,

More information

Chapter. Interest Rates. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter. Interest Rates. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Interest Rates McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Interest Rates Our goal in this chapter is to discuss the many different interest rates that

More information

Bonds and Yield to Maturity

Bonds and Yield to Maturity Bonds and Yield to Maturity Bonds A bond is a debt instrument requiring the issuer to repay to the lender/investor the amount borrowed (par or face value) plus interest over a specified period of time.

More information

Structured Finance. Fixed Income

Structured Finance. Fixed Income Structured Finance-1 Structured Finance: Fixed Income Prof. Ian Giddy New York University Structured Finance Asset-backed securitization Corporate financial restructuring Structured financing techniques

More information